An Equivalence Class of Gradual Semantics

Assessing argument strength is a key step in an argumentation process, therefore a plethora of methods, called semantics, have been developed for the purpose. Their comparison can be carried out using two complementary formal tools: the formal properties they satisfy and the ranking they produce. It has been shown that the two gradual semantics \(\texttt{Mbs}\) and \(\texttt{EMbs}\) are strongly equivalent, i.e., they return the same ranking of arguments when applied to flat argumentation graphs. This paper goes even further by characterizing the whole equivalence class to which they belong. It shows that every instance of the class is based on a numerical series and refines the ranking provided by the grounded semantics. We discuss an instance, hence novel semantics, of the class.